Compare and contrast these two assignments. Both target an 8th grade standard on seeing structure in an expression and being able to represent that expression in different ways. Which do you suppose is more common in middle school math in the United States?
A: Factor completely, and state for each stem what type of factoring you are using.
x4 + x3 - 6x2
B: Create expressions that can be factored according to the following criteria. Explain the process you used to create your expression.
A quadratic trinomial with a leading coefficient of 1 that can first be factored using greatest common factoring. The greatest common factor should be 2x.
I think you know what I’m going to tell you. By and large, middle school math instruction looks a lot more like assignment A than assignment B, according to a new analysis released this morning by the Education Trust.
While middle school teachers have largely embraced the leaner, more-focused Common Core State Standards, many math assignments prioritize procedures and algorithms at the expense of conceptual thinking and argumentation, says the report, which raises fresh questions about the challenges to upgrading math instruction in the crucial grades 6-8.
It’s the latest in a series of reports Education Trust has put out looking at whether the assignments given to students truly match the demands of new content standards shared across states. (Fewer states use the common-core standards outright than when they were rolled out in 2010, since many states have by now tweaked or revised them. But many of the common core’s tenets remain embedded in state expectations.)
Although there is a general trend of states, districts, and advocates paying much more attention to the content of curricula than a few decades ago, the Education Trust argues that educators need to go further to analyze the types of practice they give students to master content.
“What we ask kids to do—the assignments we give them—really matter, and we don’t think we’re paying enough attention to those,” said Keith Dysarz, the group’s director of P-12 practice. “A lot of times we look at student work and think about what students did, but we think you have to spend equal time looking at what you are asking them to do.”
Few Math Assignments Demand Conceptual Thinking
The new analysis looks at 1,850 different math assignments—everything from simple “exit tickets,” which teachers use to gauge understanding of a lesson in the last few minutes of class—to homework and more extended projects. The assignments were collected over a two-week period from 63 teachers working in 12 different middle schools located in six districts using the common core. The districts represent both urban and rural, and some had spent lots of money on new, aligned curricula, while others had left it up to teachers to craft.
Most of the assignments, 73 percent, did match at least one grade or course-appropriate common-core math standard; many matched more than one. That’s good news, since it indicates that teachers have embraced the standards and the way they interlock. But the assignments often did not require strategic or extended thinking. Here’s a summary of what the Education Trust found on different types of rigor:
Fewer than a third of the assignments. required students to communicate their understanding using the language of math, and only 5 percent were structured so as to stimulate discussion with peers.
There are a few possible reasons for this, Dysarz said. One is that over a few weeks, teachers may not be gradually increasing the rigor of practice assignments as students work toward a larger, “culminating” lesson. Another is that there is still a gap between new curricula and actual classroom practice that fully targets the standards. A third, and the most troubling, is that, particularly in low-income schools, the tendency is simply to give easier assignments to students who are further behind, rather than scaffolding harder assignments. (The group did find a gap in rigor between assignments at high- and low-income high schools).
To those reasons I’d suggest a fourth: I wonder if teachers, who themselves were probably taught in procedural ways, also struggle with the cognitive demand of creating these harder assignments. (I would have had a really tough time with assignment B, above.) This reminds me of a story I wrote way back in 2012, when several mathematicians told me that the first professional development teachers would need to execute the standards was simply to become more comfortable with math themselves.
Read the whole report for more data and examples of higher- and lower-rigor assignments. And concurrent with this report, the Education Trust is putting out a tool that teachers can use to analyze their own assignments and where they may be falling short.
Image: The Education Trust
A version of this news article first appeared in the Curriculum Matters blog.